Example. Use the Prime Number Theorem to estimate the number of primes less than By the Prime Number Theorem, π() ≈ ln ≈ The actual number of primes less than is π() = On the other hand, many problems concerning the distribution of primes are unsolved. For example. A Friendly Introduction to Number Theory by Joseph H. Silverman. (This is the easiest book to start learning number theory.) Level B: Elementary Number Theory by David M Burton. The Higher Arithmetic by H. Davenport. Elementary Number Theory by Gareth A. Jones. Level C: An introduction to the theory of numbers by Niven, Zuckerman, Montgomery. Get this book in print. Springer Shop; lattice points least prime Leo Moser London Math lower bound Makowski Math Mersenne primes modulo Monthly nombres notes number of primes number of solutions Number Theory partition Paul Erdös positive integers prime factors prime numbers primitive Proc proof proved pseudoprimes quadratic residues R. L. These notes serve as course notes for an undergraduate course in number the-ory. Most if not all universities worldwide offer introductory courses in number theory for math majors and in many cases as an elective course. The notes contain a useful introduction to important topics that need to be ad-dressed in a course in number theory.

I will mostly follow K.H. Rosen, Elementary Number Theory, Addison-Wesley, ISBN , but I will not require students to purchase the book! Another very good book, which is available free of charge, is by William Stein Elementary Number Theory: Primes, Congruences, and Secrets. We will use this book in particular for Sage examples. The approach in this page book tends to be more sophisticated than other books for the first number theory course, but it motivates much of the material with public key cryptography. It also uses Sage in order to deal with more realistic examples—such as RSA codes based on . Number theory has a long and distinguished history and the concepts and problems relating to the subject have been instrumental in the foundation of much of mathematics. In this book, Professor Baker describes the rudiments of number theory in a concise, simple and direct.. manner. I am quoting from the nice book "The development of Prime Number Theory" by W. Narkiewicz, Springer (), pg. 8. Any infinite sequence of pairwise coprime positive integers leads to .

It is a pleasure to read this booklet, written by experts of number theory. Due to the many results, the elegant proofs, and the informal explanations of ideas, it is highly recommended to study this small monograph thoroughly Zentralblatt MATH. From reviews of the French edition This is a short introductory book on analytic number theory.